# std::transform_inclusive_scan

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< cpp‎ | algorithm

Defined in header `<numeric>` |  |
template< class InputIt, class OutputIt, class BinaryOp, class UnaryOp > OutputIt transform_inclusive_scan ( InputIt first, InputIt last, OutputIt d_first, BinaryOp binary_op, UnaryOp unary_op ); | (1) | (since C++17) (constexpr since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOp, class UnaryOp > ForwardIt2 transform_inclusive_scan ( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOp binary_op, UnaryOp unary_op ); | (2) | (since C++17)
template< class InputIt, class OutputIt, class BinaryOp, class UnaryOp, class T > OutputIt transform_inclusive_scan ( InputIt first, InputIt last, OutputIt d_first, BinaryOp binary_op, UnaryOp unary_op, T init ); | (3) | (since C++17) (constexpr since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOp, class UnaryOp, class T > ForwardIt2 transform_inclusive_scan ( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOp binary_op, UnaryOp unary_op, T init ); | (4) | (since C++17)

1) Computes the inclusive prefix sum using op.
For each integer i in `[`​0​`,` std::distance(first, last)`)`, performs the following operations in order:

1. Creates a sequence which is formed by the values transformed from the elements of `[`first`,` iter`]` in order by unary_op, where iter is the next ith iterator of first.
2. Computes the generalized noncommutative sum of the sequence over binary_op.
3. Assigns the result to *dest, where dest is the next ith iterator of d_first.

3) Same as (1), but each sequence created is formed by init followed by the elements of `[`first`,` iter`]` in order.
2,4) Same as (1,3), but executed according to policy.
These overloads participate in overload resolution only if all following conditions are satisfied:

std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> is true. | (until C++20)
std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>> is true. | (since C++20)

The generalized noncommutative sum of a sequence of elements over a binary operation binary_op is defined as follows:

- If the sequence only has one element, the sum is the value of the element.
- Otherwise, performs the following operations in order:

1. Selects any two adjacent elements elem1 and elem2 from the sequence.
2. Calculates binary_op(elem1, elem2) and replaces the two elements in the sequence with the result.
3. Repeats steps 1 and 2 until there is only one element in the sequence.

The result is non-deterministic if the binary_op is not associative (such as floating-point addition).

For overloads (1,2), if binary_op(unary_op(*first), unary_op(*first)) is not convertible to the value type of decltype(first), the program is ill-formed.

For overloads (3,4), if any of the following values is not convertible to `T`, the program is ill-formed:

- binary_op(init, init)
- binary_op(init, unary_op(*first))
- binary_op(unary_op(*first), unary_op(*first))

If any of the following conditions is satisfied, the behavior is undefined:

- For overloads (1,2), the value type of decltype(first) is not MoveConstructible.
- For overloads (3,4), `T` is not MoveConstructible.
- unary_op or binary_op modifies any element of `[`first`,` last`)`.
- unary_op or binary_op invalidates any iterator or subrange of `[`first`,` last`]`.

### Parameters

first, last | - | the range of elements to sum
d_first | - | the beginning of the destination range; may be equal to first
policy | - | the execution policy to use
init | - | the initial value
unary_op | - | unary FunctionObject that will be applied to each element of the input range. The return type must be acceptable as input to binary_op.
binary_op | - | binary FunctionObject that will be applied in to the result of unary_op, the results of other binary_op, and init if provided
Type requirements
- `InputIt` must meet the requirements of LegacyInputIterator.
- `OutputIt` must meet the requirements of LegacyOutputIterator.
- `ForwardIt1, ForwardIt2` must meet the requirements of LegacyForwardIterator.

### Return value

Iterator to the element past the last element written.

### Complexity

Given \(\scriptsize N\)N as std::distance(first, last):

1-4) \(\scriptsize O(N)\)O(N) applications of unary_op and binary_op respectively.

### Exceptions

The overloads with a template parameter named `ExecutionPolicy` report errors as follows:

- If execution of a function invoked as part of the algorithm throws an exception and `ExecutionPolicy` is one of the standard policies, std::terminate is called. For any other `ExecutionPolicy`, the behavior is implementation-defined.
- If the algorithm fails to allocate memory, std::bad_alloc is thrown.

### Notes

unary_op is never applied to init.

The parameter init appears last, differing from std::transform_exclusive_scan, because it is optional for this function.

### Example

Run this code

    #include <functional>
    #include <iostream>
    #include <iterator>
    #include <numeric>
    #include <vector>

    int main()
    {
        std::vector data{3, 1, 4, 1, 5, 9, 2, 6};

        auto times_10 = [](int x) { return x * 10; };

        std::cout << "10 times exclusive sum: ";
        std::transform_exclusive_scan(data.begin(), data.end(),
                                      std::ostream_iterator<int>(std::cout, " "),
                                      0, std::plus<int>{}, times_10);
        std::cout << "\n10 times inclusive sum: ";
        std::transform_inclusive_scan(data.begin(), data.end(),
                                      std::ostream_iterator<int>(std::cout, " "),
                                      std::plus<int>{}, times_10);
        std::cout << '\n';
    }

Output:

    10 times exclusive sum: 0 30 40 80 90 140 230 250
    10 times inclusive sum: 30 40 80 90 140 230 250 310

### See also

partial_sum | computes the partial sum of a range of elements (function template)
transform | applies a function to a range of elements, storing results in a destination range (function template)
inclusive_scan (C++17) | similar to std::partial_sum, includes the ith input element in the ith sum (function template)
transform_exclusive_scan (C++17) | applies an invocable, then calculates exclusive scan (function template)

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